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Multifractals and 1/ƒ Noise by Benoit B. Mandelbrot Pdf
Mandelbrot is a world renowned scientist, known for his pioneering research in fractal geometry and chaos theory. In this volume, Mandelbrot defends the view that multifractals are intimately interrelated through the two fractal themes of "wildness" and "self-affinity". This link involves a powerful collection of technical tools, which are of use to diverse scientific communities. Among the topics covered are: 1/f noise, fractal dimension and turbulence, sporadic random functions, and a new model for error clustering on telephone circuits.
Gaussian Self-Affinity and Fractals by Benoit Mandelbrot Pdf
This third volume of the Selected Works focusses on a detailed study of fraction Brownian motions. The fractal themes of "self-affinity" and "globality" are presented, while extensive introductory material, written especially for this book, precedes the papers and presents a number of striking new observations and conjectures. The mathematical tools so discussed will be valuable to diverse scientific communities.
Fractals and Multifractals in Ecology and Aquatic Science by Laurent Seuront Pdf
Ecologists sometimes have a less-than-rigorous background in quantitative methods, yet research within this broad field is becoming increasingly mathematical. Written in a step-by-step fashion, Fractals and Multifractals in Ecology and Aquatic Science provides scientists with a basic understanding of fractals and multifractals and the techniques for utilizing them when analyzing ecological phenomenon. With illustrations, tables, and graphs on virtually every page – several in color – this book is a comprehensive source of state-of-the-art ecological scaling and multiscaling methods at temporal and spatial scales, respectfully ranging from seconds to months and from millimeters to thousands of kilometers. It illustrates most of the data analysis techniques with real case studies often based on original findings. It also incorporates descriptions of current and new numerical techniques to analyze and deepen understanding of ecological situations and their solutions. Includes a Wealth of Applications and Examples This book also includes nonlinear analysis techniques and the application of concepts from chaos theory to problems of spatial and temporal patterns in ecological systems. Unlike other books on the subject, Fractals and Multifractals in Ecology and Aquatic Science is readily accessible to researchers in a variety of fields, such as microbiology, biology, ecology, hydrology, geology, oceanography, social sciences, and finance, regardless of their mathematical backgrounds. This volume demystifies the mathematical methods, many of which are often regarded as too complex, and allows the reader to access new and promising concepts, procedures, and related results.
Multi-Fractal Traffic and Anomaly Detection in Computer Communications by Ming Li Pdf
This book provides a comprehensive theory of mono- and multi-fractal traffic, including the basics of long-range dependent time series and 1/f noise, ergodicity and predictability of traffic, traffic modeling and simulation, stationarity tests of traffic, traffic measurement and the anomaly detection of traffic in communications networks. Proving that mono-fractal LRD time series is ergodic, the book exhibits that LRD traffic is stationary. The author shows that the stationarity of multi-fractal traffic relies on observation time scales, and proposes multi-fractional generalized Cauchy processes and modified multi-fractional Gaussian noise. The book also establishes a set of guidelines for determining the record length of traffic in measurement. Moreover, it presents an approach of traffic simulation, as well as the anomaly detection of traffic under distributed-denial-of service attacks. Scholars and graduates studying network traffic in computer science will find the book beneficial.
Multifractal Volatility by Laurent E. Calvet,Adlai J. Fisher Pdf
Calvet and Fisher present a powerful, new technique for volatility forecasting that draws on insights from the use of multifractals in the natural sciences and mathematics and provides a unified treatment of the use of multifractal techniques in finance. A large existing literature (e.g., Engle, 1982; Rossi, 1995) models volatility as an average of past shocks, possibly with a noise component. This approach often has difficulty capturing sharp discontinuities and large changes in financial volatility. Their research has shown the advantages of modelling volatility as subject to abrupt regime changes of heterogeneous durations. Using the intuition that some economic phenomena are long-lasting while others are more transient, they permit regimes to have varying degrees of persistence. By drawing on insights from the use of multifractals in the natural sciences and mathematics, they show how to construct high-dimensional regime-switching models that are easy to estimate, and substantially outperform some of the best traditional forecasting models such as GARCH. The goal of Multifractal Volatility is to popularize the approach by presenting these exciting new developments to a wider audience. They emphasize both theoretical and empirical applications, beginning with a style that is easily accessible and intuitive in early chapters, and extending to the most rigorous continuous-time and equilibrium pricing formulations in final chapters. Presents a powerful new technique for forecasting volatility Leads the reader intuitively from existing volatility techniques to the frontier of research in this field by top scholars at major universities The first comprehensive book on multifractal techniques in finance, a cutting-edge field of research
Multifractal Analysis in Hydrology by Pietro Bernardara,Michel Lang,Eric Sauquet,Daniel Schertzer,Ioulia Tchiriguyskaia Pdf
This book provides a simplified description of the procedures to be used to perform an analysis of hydrological data within a multifractal framework. After a review of multifractal theory and the presentation of one model for identifying scale invariance properties, examples of applications to rainfall and discharge time series are given. It will be of interest to teachers and researchers in this field, both nationally and abroad.
Fractals and Disordered Systems by Armin Bunde,Shlomo Havlin Pdf
Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In ten chapters written by leading experts in the field, the reader is introduced to basic concepts and techniques in disordered systems and is led to the forefront of current research. This second edition has been substantially revised and updates the literature in this important field.
Time Series Analysis in Seismology by Alejandro Ramírez-Rojas,Leonardo Di G. Sigalotti,Elsa Leticia Flores Márquez,Otto Rendón Pdf
Time Series Analysis in Seismology: Practical Applications provides technical assistance and coverage of available methods to professionals working in the field of seismology. Beginning with a thorough review of open problems in geophysics, including tectonic plate dynamics, localization of solitons, and forecasting, the book goes on to describe the various types of time series or punctual processes obtained from those systems. Additionally, the book describes a variety of methods and techniques relating to seismology and includes a discussion of future developments and improvements. Time Series Analysis in Seismology offers a concise presentation of the most recent advances in the analysis of geophysical data, particularly with regard to seismology, making it a valuable tool for researchers and students working in seismology and geophysics. Presents the necessary tools for time series analysis as it relates to seismology in a compact and consistent manner Includes a discussion of technical resources that can be applied to time series data analysis across multiple disciplines Describes the methods and techniques available for solving problems related to the analysis of complex data sets Provides exercises at the end of each chapter to enhance comprehension
Just 23 years ago Benoit Mandelbrot published his famous picture of the Mandelbrot set, but that picture has changed our view of the mathematical and physical universe. In this text, Mandelbrot offers 25 papers from the past 25 years, many related to the famous inkblot figure. Of historical interest are some early images of this fractal object produced with a crude dot-matrix printer. The text includes some items not previously published.
This new book uses advanced signal processing technology to measure and analyze risk phenomena of the financial markets. It explains how to scientifically measure, analyze and manage non-stationarity and long-term time dependence (long memory) of financial market returns. It studies, in particular, financial crises in persistent financial markets, such as stock, bond and real estate market, and turbulence in antipersistent financial markets, such as anchor currency markets. It uses Windowed Fourier and Wavelet Multiresolution Analysis to measure the degrees of persistence of these complex markets, by computing monofractal Hurst exponents and multifractal singularity spectra. It explains how and why financial crises and financial turbulence may occur in the various markets and why we may have to reconsider the current wave of term structure modeling based on affine models. It also uses these persistence measurements to improve the financial risk management of global investment funds, via numerical simulations of the nonlinear diffusion equations describing the underlying high frequency dynamic pricing processes.
Dynamical Cognitive Science by Lawrence M. Ward Pdf
An introduction to the application of dynamical systems science to the cognitive sciences. Dynamical Cognitive Science makes available to the cognitive science community the analytical tools and techniques of dynamical systems science, adding the variables of change and time to the study of human cognition. The unifying theme is that human behavior is an "unfolding in time" whose study should be augmented by the application of time-sensitive tools from disciplines such as physics, mathematics, and economics, where change over time is of central importance. The book provides a fast-paced, comprehensive introduction to the application of dynamical systems science to the cognitive sciences. Topics include linear and nonlinear time series analysis, chaos theory, complexity theory, relaxation oscillators, and metatheoretical issues of modeling and theory building. Tools and techniques are discussed in the context of their application to basic cognitive science problems, including perception, memory, psychophysics, judgment and decision making, and consciousness. The final chapter summarizes the contemporary study of consciousness and suggests how dynamical approaches to cognitive science can help to advance our understanding of this central concept.
Fractals and Scaling in Finance by Benoit B. Mandelbrot Pdf
Mandelbrot is world famous for his creation of the new mathematics of fractal geometry. Yet few people know that his original field of applied research was in econometrics and financial models, applying ideas of scaling and self-similarity to arrays of data generated by financial analyses. This book brings together his original papers as well as many original chapters specifically written for this book.
Scaling, Fractals and Wavelets by Patrice Abry,Paolo Goncalves,Jacques Levy Vehel Pdf
Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling — self-similarity, long-range dependence and multi-fractals — are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.
Gravitation and Cosmology: From the Hubble Radius to the Planck Scale by Richard L. Amoroso,G. Hunter,Menas Kafatos,J.P. Vigier Pdf
Jean-Pierre Vigier continually labeled one of les heretiques de la science, l’eternel resistant et le patriarche is yet a pillar of modern physics and mathematics, with one leg firmly planted in theory and the other in empiricism spanning a career of nearly 60 years with a publication vitae quickly approaching 400! He wrote of his mentor Louis de Broglie “Great physicists fight great battles”, which perhaps applies even more so to 1 Jean-Pierre Vigier himself . If fortune allows a visit to Paris, reported to be the city of love, and certainly one of the most beautiful and interesting cities in the world; one has been treated to a visual and cultural feast. For example a leisurely stroll from the Musee du Louvre along the Champs-Elysees to the Arc de Triomphe would instill even the least creative soul with the entelechies of a poets muse. It is perhaps open to theoretical interpretation, but if causal conditions have allowed one to be a physicist, visiting Paris, one may have taken opportunity to visit the portion of the old Latin quarter in place Jussieu where Pierre et Marie Curie Universite, reported to be ‘the best university in France’, is stationed.